When we are in a car or even on a bicycle, our speed tends to decrease just as we near a corner, this happens because as we turn, the likelihood of our tires slipping increases with vehicle speed hence the need to slowly down; hence the adaptation of brake pads that adjusts speed. It is noticeable that, anytime it rains, you are forced to decelerate while going around a corner than under normal circumstances; this is due to a decrease in frictional force assisting in making turns.
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In this article, we will cover the concept of banking on the roads Physics class 11 which comes under under the chapter Laws of Motion. It is essential for board exams and also for competitive exams like the Joint Entrance Examination (JEE Main), National Eligibility Entrance Test (NEET), and other entrance exams such as SRMJEE, BITSAT, WBJEE, BCECE, and more. Over the last ten years of the JEE Main exam (from 2013 to 2023), a total of two questions have been asked on this concept. And for NEET one questions were asked from this concept.
Banking of road definition: It is the phenomenon in which the outer borders of the curved roads banked are raised above the inner edge to provide the necessary centripetal force to the cars for them to make a safe turn.
The outer border of a road is pushed up such that it is higher than the inner edge during a turn, and the road's surface seems to be a slightly inclined plane. This is referred to as road banking. The banking angle is the angle formed by the surface with the horizontal, i.e. the angle of inclination. When driving down such a curvy road, it's important to keep your eyes on the road.
There is a horizontal component to the normal force pressing on the vehicle. This component produces the centripetal force required to keep the vehicle from skidding.
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The vertical component of the road's normal force on a vehicle balances its weight in the absence of friction, while the horizontal component provides the centripetal force towards the road's center of curvature. The applied load N on a body of mass m traveling with velocity v along a curved road with a banking angle formula can be split into two perpendicular components.
The weight
The centripetal force is provided by the horizontal component
Equation (2) is divided by (1),
This is the greatest velocity at which an object can remain in a curved path.
From figure,
Angle of Banking
Where
Maximum speed on a banked frictional road
A vehicle must turn on a flat surface if the banking angle is zero. Because the normal force is vertical and balances the vehicle's weight, it can no longer contribute to the centripetal force. There is no way to turn if the surface is smooth. The friction force can only provide the centripetal force on a rough surface. The forces' vertical components counterbalance each other.
(i) Frictional Force
For the vehicle to keep moving in a circular path there is a force that acts between the tires of the vehicle and the road surface. This force is called the frictional force of banking roads. The frictional force in the banking of curved roads ensures the safe turning of the vehicle on curved paths and turns. Frictional force can be expressed in general as
(ii) Normal Force
The perpendicular force supporting the vehicle's weight on a banked road is called normal force. The normal force has two components:
The equation for the vertical component:
The equation for the horizontal component:
(iii) Centripetal Force
It is the force that causes angular or circular motion by pulling or pushing an object toward the center of a circle as it travels.
Another phrase used is banked turn, which is described as a turn or direction change in which the vehicle inclines towards the inside. The bank angle is the angle at which the vehicle is inclining. At the longitudinal and horizontal axes, there is an inclination. The equation for centripetal force on a banked road;
Banking is a technique for giving a vehicle the necessary centripetal force to make a safe turn on a curved route.
Skidding can be avoided by banking.
Overturning or toppling is less likely when roads are banked.
1. Bankng of curves needs more space which makes it difficult in urban areas.
2. Heavy vehicles need more friction than banking can provide thus making it less effective.
3. Constructing banked roads is more expensive compared to flat roads.
Example 1: A circular road of radius 30 m has banking at an angle of
1) 30
2) 20
3) 35
4) 45
Solution :
Maximum speed on a banked frictional road
maximum speed with the banked road with the friction is
Hence, the answer is option (1).
Example 2: Statement I: A cyclist is moving on an unbanked road with a speed of -1 7 km-1 and takes a sharp circular turn along the path of a radius of 2m without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip and pass the curve ( g= 9.8 m/s2)
Statement II: If the road is banked at an angle of
1) Statement I is correct and Statement II is incorrect.
2) Both statement I and statement II are false.
3) Both statement I and statement II are true.
4) Statement I is incorrect and statement II is correct.
Solution :
A cyclist is moving on an unbanked road with a speed of 7 km/h
Since the cyclist is riding at a safer speed of 7km/h, Statement I is correct.
For statement II
The speed of the cyclist is
The sa peed of a cyclist is between the safe limit of
So, both statement I and statement II are true.
Hence, the answer is the option(3).
Example 3: A turn of radius 20 m is banked for the vehicle going to a speed of
1) 1
2) 0.5
3) 0.75
4) 0.25
Solution :
From figure,
For small angle
Hence, the answer is option (1).
Example 4: The normal reaction '
1) 10.2
2) 7.2
3) 12.4
4) 6.96
Solution:
For maximum possible speed,
Along X-axis:
Along Y-axis:
From Eqn (1)
Hence, the answer is option (1).
Example 5: A car of mass 2000kg going round a banked curved a radius 40m on a frictionless road. If the banking angle is 450, the speed of the car is :
1) 10m/s
2) 15m/s
3) 20m/s
4) 25m/s
Solution:
Banking of Road -
From figure
Hence, the answer is option (3).
Also read -
Banking of roads is the phenomenon in which the outer borders of why are curved roads banked are raised above the inner edge to provide the necessary centripetal force to the cars in order to make a safe turn.
A vehicle must turn on a flat surface if the banking angle is zero. Because the normal force is vertical and balances the vehicle's weight, it can no longer contribute to the centripetal force. There is no way to turn if the surface is absolutely smooth. The friction force can only provide the centripetal force on a rough surface. The forces' vertical components counterbalance each other.
A vehicle must turn on a flat surface if the banking angle is zero. Because the normal force is vertical and balances the vehicle's weight, it can no longer contribute to the centripetal force. There is no way to turn if the surface is absolutely smooth. The friction force can only provide the centripetal force on a rough surface. The forces' vertical components counterbalance each other.
Banking is a technique for giving a vehicle the necessary centripetal force to make a safe turn on a curved route.
Skidding can be avoided by banking.
Overturning or toppling is less likely when roads are banked.
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